Question: Simplify the following expression: $\sqrt{54}+\sqrt{96}+\sqrt{150}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{54}+\sqrt{96}+\sqrt{150}$ $= \sqrt{9 \cdot 6}+\sqrt{16 \cdot 6}+\sqrt{25 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{6}+\sqrt{16} \cdot \sqrt{6}+\sqrt{25} \cdot \sqrt{6}$ $= 3\sqrt{6}+4\sqrt{6}+5\sqrt{6}$ Finally, simplify by combining the terms. $= ( 3 + 4 + 5 )\sqrt{6} = 12\sqrt{6}$